Overture

This notebook reproduces the results from Weng et al.

It is highly recommended for the reader to familiarize oneself with the paper before proceeding. This is basically a pure reproduction, without a lot of explanations or context.

All in all I'd say that reproducing the results was relatively straightforward, if time-consuming as mimicking the original figures took several lines of code. I guess that can be construed as the original paper being a solid piece of work.

Anyhow, the most challenging part was without a doubt calculating the resistance, as it required clipping the HPPC cycle in a very specific manner. I'm glad I was finally able to crack that.

%matplotlib inline

import voltaiq_studio as vs

import figures
import utils

Dataset

Load in all data from UMich

trs = vs.get_test_records()
um_dataset = [tr for tr in trs if('UM ' in tr.name)]

The dataset contains two categories, each containing two subcategories (I made it in draw.io, modeling figure S1a in the original paper):

We're going to store them in a dict as follows

• name: str

-- cycling: pd.DataFrame

-- formation: pd.DataFrame

-- high_temperature: bool (45 or ambient)

-- fast_formation: bool (fast or normal)}

-- (some others are added later on)

keys = ['cycling', 'high_temperature', 'fast_formation']
no_formation_cycles = 10

trace_keys = utils.get_json("trace_keys")

categorized_experiments = dict()
formations = dict()
for experiment in um_dataset:
    serial_no = utils.generate_exp_id(name=experiment)
    df = utils.load_data_by_experiment(
        experiment=experiment,
        trace_keys=trace_keys['trace_keys']
    )
    
    if experiment.total_cycles < no_formation_cycles:  # Formation
        df_zero_shifted = utils.zero_shift_formation(df)
        formations[serial_no] = df_zero_shifted
        continue

    temperature = 1 if 'HT' in experiment.name else 0 
    formation = 1 if 'Micro' in experiment.name else 0
    
    data = dict(zip(keys, [df, temperature, formation]))
    categorized_experiments[serial_no] = data

categorized_experiments = utils.match_cycling_with_formation(
    categorized_experiments,
    formations
)

Figure 1: Fast formation superior to baseline formation

Figure implementation

fig1 = figures.Figure1()
NOMINAL_CAPACITY = 0.236  # Ah

categorized_cycles_to_70 = [[[], []], [[], []]]  # aa thic is awful. Should be three boolean columns!
for i, (cell_id, params) in enumerate(categorized_experiments.items()):

    # Grouping
    by_cycle = params['cycling'].groupby(by='h_cycle').max()
    discharge_capacity = by_cycle.h_discharge_capacity.to_numpy()
    cycles_to_70 = sum(discharge_capacity > 0.7*NOMINAL_CAPACITY)

    # Figure logic
    c = 'red' if params['high_temperature'] else 'blue'
    c = c if params['fast_formation'] else 'k'
    x_pos = 0 if params['fast_formation'] else 1
    row = 1 if params['high_temperature'] else 0
    linestyle = 'solid' if params['fast_formation'] else 'dotted'

    categorized_experiments[cell_id]['cycles_to_70'] = cycles_to_70
    categorized_cycles_to_70[row][x_pos].append(cycles_to_70)

    fig1.scatterplot(
        cycles_to_70=cycles_to_70,
        row=row,
        x_pos=x_pos,
        shifter=i,
        c=c
    )

    # Line plot on left
    hppc_indices = utils.filter_HPPC(by_cycle=by_cycle, threshold=0.1)
    cycles_w_hppc = []
    for i in range(2, len(hppc_indices)):
        # This is a little hacky but does the job.
        # Skips the embedded reference performance tests
        if abs(hppc_indices[i-1] - hppc_indices[i]) < 10:
            continue

        fig1.lineplot(
            discharge_capacity=discharge_capacity,
            hppc_indices=hppc_indices,
            i=i,
            c=c,
            linestyle=linestyle,
            row=row
        )

legend_colors = ['b', 'r']
legend_title = ['Room Temperature,\n1C/1C, 3.0V—4.2V',
                '45°C,\n1C/1C, 3.0V—4.2V']

for row in range(2):
    fig1.legend(
        legend_title=legend_title[row],
        c=legend_colors[row],
        row=row
    )

    for col in range(2):
        x_pos = col
        fig1.boxplot(
            row=row,
            x_pos=x_pos,
            categorized_cycles_to_70=categorized_cycles_to_70
        )

    fig1.capacity_fade_line(row=row)
    fig1.properties(row=row)


fig1.showme()

Original figure:

---

Let's see whether there's a statistically significant difference in the cycling performance between the two protocols.

The original paper reports $p<0.001$ for both temperatures. However, exact values are not specified.

for temperature in range(2):
    p_val = utils.get_p_val(
        var_1=categorized_cycles_to_70[temperature][0],
        var_2=categorized_cycles_to_70[temperature][1]
    )
    print("{:.1E}".format(p_val))

3.7E-06
3.4E-03

Both p-values are in agreement with the original findings.

---

Before going any further we should look at the two formation protocols.

titles = ['Baseline', 'Fast']
no_curves = len(categorized_experiments)
no_cols = 2
formation_fig = figures.FormationFigure(no_cols=no_cols, no_curves=no_curves)

for i, (_, params) in enumerate(categorized_experiments.items()):
    col = 1 if params['fast_formation'] else 0
    df = params['formation']

    formation_fig.lineplot(col=col, df=df, i=i)

formation_fig.properties(no_cols=no_cols, titles=titles)

formation_fig.showme()

(don't mind the colormap)

and also the first few cycles after formation

adolescence_fig = figures.AdolescenceFigure(no_cols=no_cols, no_curves=no_curves)
for i, params in enumerate(categorized_experiments.values()):
    col = 1 if params['fast_formation'] else 0
    df = params['cycling']
    df = df[df.h_cycle < 5]

    adolescence_fig.lineplot(col=col, df=df, i=i)

adolescence_fig.properties(no_cols=no_cols, titles=titles)

adolescence_fig.showme()

We want to extract $V$ and $I$ from the 'jagged' charge step to calculate the resistance. It is there that the high current pulse was applied.

Figure 2

This figure is essentially two separate subfigures: The upper row is all conventional electrochemical properties, whereas the lower one contains resistance plots.

Do note that I change the color scheme a little bit. I don't particularly care for how they did it for this one.

# TODO: Remove
Q_ds = [[], []]  # Discharge capacity after formation
Q_LLIs = [[], []]  # Loss of Lithium inventory
CEs = [[], []]  # Coulombic Efficiency
Rs = []  # Cell resistance
R_5s = [[], []]
R_90s = [[], []]

for i, (cell_id, params) in enumerate(categorized_experiments.items()):
    formation_by_cycle = params['formation'].groupby(by='h_cycle').max()

    charge_capacity, discharge_capacity = utils.get_capacities(
        formation=formation_by_cycle
    )
    
    # For fig logic
    x_pos = 0 if params['fast_formation'] else 1
        
    # Q_d
    categorized_experiments[cell_id]['Q_d'] = discharge_capacity
    Q_ds[x_pos].append(discharge_capacity)

    # Q_LLI
    Q_LLI = charge_capacity - discharge_capacity
    categorized_experiments[cell_id]['Q_LLI'] = Q_LLI
    Q_LLIs[x_pos].append(Q_LLI)
    
    # CE
    CE = discharge_capacity / charge_capacity
    categorized_experiments[cell_id]['CE'] = CE
    CEs[x_pos].append(CE)
    
    # Rs
    R = utils.get_resistance(cycling=params['cycling'], to_plot=i)
    Rs.append(R)
    
    if params['high_temperature']:
        R_5 = utils.get_R5SoC(Rs=R[0:2])
        R_5s[x_pos].append(R_5)

    categorized_experiments[cell_id]['R_5'] = R_5
    categorized_experiments[cell_id]['R_90'] = R[-3]
    R_90s[x_pos].append(R[-3])


metrics = [Q_ds, Q_LLIs, CEs]

This zoomed-in figure demonstrates how we calculate $\Delta \mathrm{V}$ for each current pulse, i.e. $\color{blue}{\mathrm{V}}$ subtracted from $\color{red}{\mathrm{V}}$.

Figure implementation

fig2 = figures.Figure2()

ylabels = ['$\mathrm{Q_d}$ (Ah)',
           '$\mathrm{Q_{LLI} = Q_c - Q_c}$ (Ah)',
           '$\mathrm{CE_f (\%)}$']
x_positions = [0, 1]
colors = ['g', 'k']

for x_pos in x_positions:        
    fig2.scatterplot_lower(
        R_5SoC=R_5s[x_pos],
        x_pos=x_pos,
        c=colors[x_pos]
    )
    fig2.boxplot_lower(
        R_5SoC=R_5s[x_pos],
        x_pos=x_pos
    ) 
    for col, metric in enumerate(metrics):
        fig2.scatterplot(
            metric=metric[x_pos],
            col=col,
            x_pos=x_pos,
            c=colors[x_pos]
        )
        fig2.boxplot(
            metric=metric[x_pos],
            x_pos=x_pos,
            col=col,
            ylabel=ylabels[col]
        )
#         fig2.properties(ylabel=ylabels[col], col=col)

xlims = [[0, 100],[3, 10]]
for i, params in enumerate(categorized_experiments.values()):
    if not params['high_temperature']: 
        continue  # They only included high T cells in this fig
        
    c = 'g' if params['fast_formation'] else 'k'
    for col in range(2):
        fig2.lineplot(
            R=Rs[i],
            xlim=xlims[col],
            c=c,
            col=col
        )
        
fig2.showme()

Original figure:

Figure 3: Modeling Diagnostic Signals

Figure implementation

fig3 = figures.Figure3()

xlabels = ['$\mathrm{Q_{LLI}}$ (Ah)',
           '$\mathrm{CE_f}$ ( )',
           '$\mathrm{R_{10s,\,5\%SOC}\,(m\Omega)}$',
           '$\mathrm{R_{10s,\,90\%SOC}\,(m\Omega)}$']
xlims = [[0.20, 0.60],
         [0.8, 1.0],
         [20, 80],
         [10, 30]]  # Manual
ylabel = 'Cycles\nto 70%'

variables = ['Q_LLI', 'CE', 'R_5', 'R_90']
        
for i, params in enumerate(categorized_experiments.values()):
    c = 'red' if params['high_temperature'] else 'blue'
    c = c if not params['fast_formation'] else 'k'
    row = 1 if params['high_temperature'] else 0

    for col, variable in enumerate(variables):
        fig3.scatterplot(
            variable=params[variable],
            cycles_to_70=params['cycles_to_70'],
            row=row,
            col=col,
            c=c
        )
        fig3.properties(
            xlabel=xlabels[col],
            xlim=xlims[col],
            col=col,
            ylabel=ylabel
        )
    
fig3.showme()

Original figure (note that my axes have different limits):

All in all, my results match the original ones quite well. Any differences are minute and don't affect the statistical interpretation.